The diagram shows a logo made from 3 circles. Each logo has centre O.
What percentage of the logo is shaded blue?
You must show all your working and the final answer must include the % sign.
(From MathsWatch)

% area of the shaded region = 33%

Step-by-step explanation:

Radius of the middle circle = 7 cm

Radius of the inner circle = 4 cm

Area of the middle circle = πr²

                                          = π(7)²

                                          = 49π

   Area of the inner circle = π(4)²

                                           = 16π

Area of the shaded region= 49π - 16π

                                            = 33π

Area of the outermost circle = π(10)²

                                               = 100π

% area of the shaded region =

                                                =

                                                = 33%

Therefore, area of the shaded region is 33% of the complete logo.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.